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newSchoolWorks.com › VoTechWorks › Building & Construction › Solar / PV Installation › Photovoltaic System Design › Lesson 3
BLD-SOLA09-02 · Lesson 3 · 14 clock hours · lab

System Sizing: Loads, Array Power, and String Configuration

Objective. Students size a complete residential grid-tied PV system—array wattage, number of modules, and string configuration—for a given utility bill and site, producing a design that meets string voltage and current limits for the selected inverter.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a licensed professional engineer or master tradesperson or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.

VoTechWorks program approval and accreditation are still in progress. Credentials are issued only by the certifying bodies named in each program, after their own exams.

Why System Sizing Matters

A correctly sized PV system does two things at once: it generates enough energy to offset the customer's electricity use, and it operates safely within the electrical limits of the equipment you install. Undersizing wastes the customer's money over time; oversizing wastes it upfront and can damage the inverter. String configuration errors—exceeding the inverter's maximum input voltage or falling below its minimum operating voltage—cause equipment shutdowns, component failure, and potential fire. Getting the numbers right before you pick up a wire is a core professional skill and a tested topic on both the NABCEP PV Associate and PV Installation Professional exams.

Step 1: Determine the Average Daily Load

Start with 12 months of utility bills. Add all the monthly kWh values together, then divide by 12 to get the average monthly kWh. Divide that figure by 30.4 (the average days per month) to get the average daily kWh load. This single number becomes your design target.

Example: A customer's bills total 14,400 kWh for the year. Average monthly = 14,400 ÷ 12 = 1,200 kWh. Average daily = 1,200 ÷ 30.4 ≈ 39.5 kWh/day.

Step 2: Apply Peak Sun Hours and the Derate Factor

Peak sun hours (PSH) represent the equivalent number of hours per day that the sun shines at exactly 1,000 W/m², the standard test condition (STC) irradiance. Your site's PSH value comes from a resource such as the NREL PVWatts tool or solar maps covered in an earlier lesson.

A real system never produces its full STC nameplate output. Losses from wiring resistance, module mismatch, soiling, inverter efficiency, temperature effects, and other factors are combined into a single derate factor (also called a performance ratio). A commonly used default value is 0.80, meaning a system produces roughly 80% of what its nameplate rating predicts. Always confirm the derate factor with your design software or employer's standard; NABCEP resources discuss the components that make it up.

Required DC array wattage formula:

```

Required kW (DC) = Daily kWh load ÷ (PSH × derate factor)

```

Multiply by 1,000 to convert to watts.

Step 3: Select Modules and Calculate Module Count

Choose a module from the equipment list. Its datasheet lists the STC power rating (Watts)—this is the module's nameplate wattage. Divide your required array wattage by the module's wattage and round up to the next whole number:

```

Number of modules = Required array watts ÷ Module watts (round up)

```

Note the actual installed wattage (modules × module watts); it will typically exceed the minimum target by a small margin, which is acceptable.

Step 4: Understand String Configuration Basics

A string is a series-connected row of modules. In series, voltages add while current stays constant. The inverter sets hard electrical limits you must respect:

Step 5: Temperature-Corrected Voltage Calculations

Module voltage changes with temperature. Cold weather raises voltage; hot weather lowers it. You must check two conditions:

Cold (worst case for maximum voltage): Use the lowest expected ambient temperature for your site. Apply the module datasheet's temperature coefficient of Voc to find the highest the open-circuit voltage will reach. Multiply that corrected Voc by the number of modules in the string. This number must not exceed the inverter's absolute maximum input voltage.

Hot (worst case for minimum operating voltage): Use a high module operating temperature (modules run hotter than air temperature; a common design assumption is that module temperature can reach 70 °C or higher on a hot day). Apply the temperature coefficient of Vmp to find the lowest the maximum-power voltage will fall. Multiply the corrected Vmp by the number of modules. This number must remain above the inverter's minimum MPPT voltage so the system keeps producing power.

The string sizing worksheet guides you through both calculations column by column.

Step 6: Finalize Array Configuration

With the valid string length (minimum and maximum modules per string) established, determine how many strings run in parallel to reach your target wattage without exceeding the inverter's maximum input current. Document:

Have the instructor verify your worksheet before you move to the drafting phase.

Safety Reminders for This Lab

This is a paper and calculation lab—no live electrical work occurs today. However, understand why these limits exist: a string voltage that exceeds inverter Vmax is an arc flash and fire hazard. When you later install these systems, follow all lockout/tagout (LOTO) procedures before working on any live DC circuit. PV modules generate voltage whenever light strikes them and cannot be de-energized by switching alone; treat all module wiring as live. Wear appropriate PPE (safety glasses, insulated gloves rated for the voltage present) whenever handling energized DC wiring in the field.

Key terms10

Average daily load (kWh/day)The customer's average daily electricity consumption, calculated by dividing annual kWh usage by 365 (or average monthly usage by 30.4). It is the primary design target for system sizing.
Peak sun hours (PSH)The equivalent number of hours per day at exactly 1,000 W/m² irradiance that produces the same total solar energy as actual varying conditions at a given site. Used to translate array wattage into expected daily energy output.
Derate factor (performance ratio)A multiplier, typically around 0.80, that accounts for all real-world system losses—wiring resistance, soiling, temperature, inverter efficiency, and mismatch—reducing actual output below STC nameplate ratings.
Open-circuit voltage (Voc)The voltage across a module or string when no current is flowing, measured under standard test conditions. It is the highest voltage the string will produce and rises at low temperatures, which is the critical value for inverter maximum voltage compliance.
Maximum power point voltage (Vmp)The module voltage at which the module produces its rated peak power under STC. It decreases at high temperatures and is used to verify the string stays within the inverter's MPPT voltage window during hot weather.
MPPT voltage windowThe range of input voltages within which a string inverter's maximum power point tracker operates efficiently. A string whose operating voltage falls outside this window will produce reduced or no power.
Temperature coefficient of voltageA datasheet value, expressed as %/°C or V/°C, that quantifies how much a module's Voc or Vmp changes per degree of temperature change from STC (25 °C). A negative coefficient means voltage falls as temperature rises.
String configurationThe arrangement of modules defined by the number of modules connected in series (per string) and the number of strings connected in parallel, which together determine array voltage, current, and total wattage.
DC nameplate wattageThe total rated power output of a PV array under STC, equal to the number of modules multiplied by each module's rated wattage. It is the starting point before derate factors are applied to predict actual energy production.
Maximum input voltage (inverter Vmax)The absolute highest DC voltage a string inverter can safely accept at its input terminals. Exceeding this limit can permanently damage the inverter and creates a serious electrical safety hazard.

Worked examples4

1. A household's 12-month utility bills total 15,600 kWh. The site has 5.2 peak sun hours per day. Using a derate factor of 0.80, what DC array size (in watts) is required?
  1. Find average daily load: 15,600 kWh ÷ 12 months = 1,300 kWh/month; 1,300 ÷ 30.4 days = 42.76 kWh/day.
  2. Apply the sizing formula: Required DC kW = 42.76 kWh/day ÷ (5.2 PSH × 0.80 derate) = 42.76 ÷ 4.16 = 10.28 kW.
  3. Convert to watts: 10.28 kW × 1,000 = 10,280 W required.
Answer: The system requires approximately 10,280 W (10.28 kW) of DC nameplate capacity.
2. A module has a Voc of 45.2 V and a temperature coefficient of Voc of -0.29%/°C. The lowest expected ambient temperature at the site is -10 °C. What is the temperature-corrected Voc?
  1. Find the temperature difference from STC (25 °C): 25 °C - (-10 °C) = 35 °C below STC. Because it is colder, voltage increases.
  2. Convert the coefficient to a per-degree value: 0.29% of 45.2 V = 0.0029 × 45.2 = 0.1311 V/°C.
  3. Calculate the voltage increase: 0.1311 V/°C × 35 °C = 4.59 V increase.
  4. Temperature-corrected Voc: 45.2 V + 4.59 V = 49.79 V ≈ 49.8 V.
Answer: The temperature-corrected Voc at -10 °C is approximately 49.8 V.
3. Using the corrected Voc of 49.8 V from the previous example and an inverter with a maximum input voltage of 600 V, what is the maximum number of modules allowed in one string?
  1. Divide the inverter's maximum input voltage by the temperature-corrected Voc: 600 V ÷ 49.8 V = 12.05.
  2. Round down to the nearest whole number (never round up, because rounding up would exceed the inverter limit): 12 modules.
Answer: The maximum string length is 12 modules.
4. The required array size is 10,280 W. The selected module is rated at 400 W. Valid string length is 10–12 modules. The inverter's maximum input current is 30 A and each string's short-circuit current (Isc) is 10.5 A. How many modules are needed, and how many strings can the inverter accept?
  1. Calculate the number of modules: 10,280 W ÷ 400 W = 25.7; round up to 26 modules.
  2. Choose a string length within the valid range. Select 13 modules per string — wait, 13 exceeds the maximum of 12. Use 12 modules per string: 12 × 400 W = 4,800 W per string.
  3. Number of strings needed: 10,280 W ÷ 4,800 W = 2.14; round up to 3 strings. Total modules = 3 × 12 = 36 modules; total array = 36 × 400 W = 14,400 W. Verify this meets the target (14,400 > 10,280 ✓).
  4. Check inverter current: 3 strings × 10.5 A Isc = 31.5 A total — this exceeds the 30 A maximum. Reduce to 2 strings: 2 × 10.5 A = 21 A (within limit ✓). Two strings × 12 modules = 24 modules; 24 × 400 W = 9,600 W — slightly below target. Add a third string to a second MPPT input if the inverter has one, or select a higher-current inverter. Document the limitation on the worksheet.
Answer: With a single 30 A input, only 2 strings (24 modules, 9,600 W) are within the current limit. A code-compliant solution requires either a multi-MPPT inverter or an inverter with a higher current rating to accommodate 3 strings and reach the 10,280 W target.

The math in this lesson2

Learners compute temperature-corrected Voc and maximum modules per string under 600 V.
A-SSE.1A-CED.4
Brush up in the math halls at newSchoolWorks.com:
In class: Given 12 months of a sample utility bill, calculate the average daily kWh load and use the site's peak sun hours from the previous lesson to determine the required array DC nameplate wattage, applying a standard derate factor. · Select a module and a string inverter from a provided equipment list; calculate minimum and maximum string lengths using temperature-corrected Voc and Vmp values versus the inverter's MPPT voltage window and maximum input voltage. · Configure the array (number of strings, modules per string) to meet the target wattage without exceeding inverter limits; document the configuration on a string sizing worksheet and verify with instructor before proceeding to drafting.
Materials: Sample utility bills (instructor-prepared), module datasheets, inverter datasheets (minimum two inverter models), string sizing worksheet, scientific calculator, NABCEP PV Associate Study Guide sections on system sizing
Check: Completed string sizing worksheet reviewed by instructor; array size within 10% of instructor-calculated target, string voltage within inverter limits (no exceedance of max input voltage at low temperature), current within inverter input current rating. Pass = all three criteria met.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

System Design and Sizing
1. A customer used 13,140 kWh over the past year. What is the average daily load used for system sizing?
System Design and Sizing
2. A site has 4.5 peak sun hours per day and a derate factor of 0.80. A household requires 36.0 kWh/day. What DC array size is needed?
System Design and Sizing
3. Which condition determines the MAXIMUM string length when configuring a string inverter?
System Design and Sizing
4. A module has a rated Vmp of 38.0 V and a temperature coefficient of Vmp of -0.40%/°C. At a module operating temperature of 70 °C, what is the corrected Vmp?
Safety and Code Compliance
5. Why must temperature-corrected Voc be used—rather than the STC Voc—when calculating maximum string length?
Safety and Code Compliance
6. An installer connects a string whose cold-corrected Voc of 640 V exceeds the inverter's 600 V maximum input rating. What is the primary risk?
System Design and Sizing
7. A string inverter has an MPPT voltage window of 200–480 V and a maximum input voltage of 600 V. A string's cold-corrected Voc is 490 V and its hot-corrected Vmp is 195 V. Which statement best describes this string configuration?
System Design and Sizing
8. When configuring multiple strings in parallel to a single inverter input, which inverter specification limits the total number of strings?
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